Answer:
(E)A trapezoid
Step-by-step explanation:
Given the shape which is a rectangular based pyramid.
A cross-section is cut but it does not pass through the top vertex of the pyramid.
The shape formed will have two parallel unequal sides (the base and the top)However, the other two sides will be slant.Therefore, the shape which describes the cross-section will be a trapezoid.
Answer:
The figure is a rectangular pyramid. The cross section is perpendicular to the rectangular base and passes through the top vertex of the figure. A triangle that does not have the same dimensions as one of the faces is formed.
Step-by-step explanation:
Mr. Ferrier invested $26,000. Some was invested in bonds that made a 5% profit, and the rest was put in stocks that made an 8% profit. How much did mr. Ferrier invest in bonds if his total profit on both types of investments was $1,420
Answer:
bonds=22000
stock=4000
Step-by-step explanation:
let b for bonds , and s for stock
b+s=26000
0.05 b +0.08 s=1420
to solve (by elimination)
1- multiply first equation with 0.05 to eliminate b
0.05 b+0.05 s=1300
0.05b+0.08s=1420
subtract two equations:
0.05b+0.05s-0.05b-0.08s=1300-1420
-0.03s=-120
s=120/0.03=4000
b+s=26000
b=26000-4000=22000
check:0.05(22000)+0.08(4000)=1420
Answer:
$22000
Step-by-step explanation:
x*0.05+(26000-x)*0.08= 1420
0.05x - 0.08x + 2080= 1420
0.03x=2080 -1420
0.03x= 660
x= 660/0.03
x= 22000
$22000 = 5% bonds
$4000 = 8% stocks
ASAP! A boat travelling at top speed upstream moves at 15km/hr. When it travels downstream, again at top speed< it moves at 25km/hr. What is the boat's top speed in still water?
Answer: 20km/h
Step-by-step explanation:
20km/h. Simply average 15 and 25 by doing (15+25)/2
Hope it helps <3
How is it that it is (-11/4,-1/2) ?
Answer:
Choice 3
Step-by-step explanation:
A(-5,-1) and B(4, 1)
Distance AB is calculated as x²+y², where x= 4-(-5)=9 and y= 1-(-1)=2
Point P is at 1/4 of distance from point A, so its coordinates will be at 1/4 of full distance from A to B in term of both coordinates:
-5 + 9/4= (-20+9)/4= -11/4-1 +2/4= (-4+2)/4= -2/4= -1/2So P= (-11/4, -1/2) and choice 3
Which one of the following numbers is divisible by 11?
A. 924711
B. 527620
C. 320793.
D. 435854
Answer:
320793
Step-by-step explanation:
320793 / 11 = 29163
A soccer team scores 12 points in 5 matches. They scored the same number of points in each of their first 3 matches and one more point in each of their last 2. How many points did they score in each match?
Answer:
2 points the first 3 matches then 3 points the last 2 matches
Step-by-step explanation:
12 points in 5 matches and the first 3 are all the same then the other 2 increased by 1 point
They got 2 points the first 3 matches then 3 points the last 2 matches
2 + 2 + 2 (first 3 matches) = 6
3 + 3 (last 2 matches) = 6
6 + 6 = 12
Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean mu equals 247 days and standard deviation sigma equals 16 days. Complete parts (a) through (f) below.
Answer:
The answer is given below
Step-by-step explanation:
a) What is the probability that a randomly selected pregnancy lasts less than 242 days
First we have to calculate the z score. The z score is used to determine the measure of standard deviation by which the raw score is above or below the mean. It is given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Given that Mean (μ) = 247 and standard deviation (σ) = 16 days. For x < 242 days,
[tex]z=\frac{x-\mu}{\sigma}=\frac{242-247}{16}=-0.31[/tex]
From the normal distribution table, P(x < 242) = P(z < -0.3125) = 0.3783
(b) Suppose a random sample of 17 pregnancies is obtained. Describe the sampling distribution of the sample mean length of pregnancies.
If a sample of 17 pregnancies is obtained, the new mean [tex]\mu_x=\mu=247,[/tex] the new standard deviation: [tex]\sigma_x=\sigma/\sqrt{n} =16/\sqrt{17} =3.88[/tex]
c) What is the probability that a random sample of 17 pregnancies has a mean gestation period of 242 days or less
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{242-247}{16/\sqrt{17} }=-1.29[/tex]
From the normal distribution table, P(x < 242) = P(z < -1.29) = 0.0985
d) What is the probability that a random sample of 49 pregnancies has a mean gestation period of 242 days or less?
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{242-247}{16/\sqrt{49} }=-2.19[/tex]
From the normal distribution table, P(x < 242) = P(z < -2.19) = 0.0143
(e) What might you conclude if a random sample of 49 pregnancies resulted in a mean gestation period of 242 days or less?
It would be unusual if it came from mean of 247 days
f) What is the probability a random sample of size 2020 will have a mean gestation period within 11 days of the mean
For x = 236 days
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{236-247}{16/\sqrt{20} }=-3.07[/tex]
For x = 258 days
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{258-247}{16/\sqrt{20} }=3.07[/tex]
From the normal distribution table, P(236 < x < 258) = P(-3.07 < z < 3.07) = P(z < 3.07) - P(z < -3.07) =0.9985 - 0.0011 = 0.9939
Find the nth term -1 8 19 32 47
[tex]\bold{\text{Answer:}\quad \text{Recursive formula:}\ a_n=a_{-1}+2n+5}\\.\qquad \qquad \ \text{Explicit formula:}\ a_n=2n^2+3n-6[/tex]
Step-by-step explanation:
-1 → 8 = +9
8 → 19 = +11
19 → 32 = +13
32 → 47 = + 15
a₁ = -1
d = 2n + 5
Recursive formula is: the previous term plus the difference (d)
[tex]\large\boxed{a_n=a_{n-1}+2n+5}[/tex]
Explicit formula is the first term plus the product of d and n-1:
[tex]a_n=a_1+d(n-1)\\a_n=-1+(2n+5)(n-1)\\a_n=-1+2n^2-2n+5n-5\\\large\boxed{a_n=2n^2+3n-6}[/tex]
Evaluate: m - 12 when m = 23.
Answer:
11
Step-by-step explanation:
sub 23 with m
23 - 12 = 11
A small community organization consists of 20 families, of which 4 have one child,8 have two children, 5 have three children, 2 have four children, and 1 has fivechildren. If one of these families is chosen at random, what is the probability it has`children,`= 1,2,3,4,5?
Answer and Step-by-step explanation:
According to the situation, The probabilities for each one is given below:
As there are 20 families
So the probabilities for each one is
For four families have one child is
[tex]= \frac{4}{20}\\\\ = \frac{1}{5}[/tex]
For eight families have two children is
[tex]= \frac{8}{20}\\\\ = \frac{2}{5}[/tex]
For five families have three children is
[tex]= \frac{5}{20}\\\\ = \frac{1}{4}[/tex]
For two families have four children is
[tex]= \frac{2}{20}\\\\ = \frac{1}{10}[/tex]
For one family have five children is
[tex]= \frac{1}{20}[/tex]
Find the value of x. Round the length to the nearest tenth.
Answer:
[tex] x = 5.1 yd [/tex]
Step-by-step Explanation:
Angle of depression is congruent to angle of elevation.
Therefore, angle of elevation of the given figure, which is opposite to x is 25°.
Adjacent length = 11 yd
Opposite length = x
Trigonometric ratio formula for finding x is shown below:
[tex] tan(25) = \frac{opposite}{adjacent} [/tex]
[tex] tan(25) = \frac{x}{11} [/tex]
Multiply both sides by 11 to solve for x
[tex] 11*tan(25) = x [/tex]
[tex] 5.129 = x [/tex]
[tex] x = 5.1 yd [/tex] (to the nearest tenth)
If you are given the graph of h(x) = log6x, how could you graph M(x) = log6(x+3)?
Answer:
Translate 3 units to the left
Step-by-step explanation:
CD=17 AM=5 CD=? I've tried everything but I can't figure it out.
Answer:
We can prove that ΔTMB ≅ ΔTMD and ΔTMA ≅ ΔTMC by ASA. This means that BM = MD = BD / 2 = 8.5 and that AM = CM = 5 which means that CD = MD - CM = 8.5 - 5 = 3.5.
Anyone know please help!!
Answer:
only the inverse is a function
Find the values of the variables and the measures of the angles
Answer:
Add each given variable
(6x + 10) + (x + 2) + x = 8x + 12
The sum of all the angles equals 180ᴼ
8x + 12 = 180
Subtract 12 from both sides
8x = 168
Divide by 8 on both sides
x = 21
Now plug in 21 for each x to find the measure of each angle.
(6[21] + 10) = 126 + 10 = 136ᴼ
(21 + 2) = 23ᴼ
x = 21ᴼ
Please answer this question fast in two minutes
Answer:
132 degree
Step-by-step explanation: angle kjh is 132 degree and since lk is a straight line it is 180 degree. angle kjh is 132 degree so, angle LJM is 132 degree. This is because adjacent angles are equal as you can see, Angle LJM is adjacent to Angle KJH.
SNOG HELP OR SOMEONE THANK YOUUUU
Which unit rate is equivalent to 14 miles per gallon?
two gallons over thirty two miles
thirty two miles over two gallons
three gallons over forty two miles
forty two miles over three gallons
Answer:
forty two miles over three gallons
Step-by-step explanation:
2 gallons over 32 miles simplifies to 1 gallon over 16 miles, or 1 gallon per 16 miles. This is not the desired result, so we know the first choice is incorrect.
32 miles over 2 gallons simplifies to 16 miles over 1 gallon, or 16 miles per gallon. Again, this is not the desired result, so we know the second choice is also incorrect.
3 gallons over 42 miles simplifies to 1 gallon over 14 miles, or 1 gallon per 14 miles. While this may look correct, note that 1 gallon per 14 miles and 14 miles per gallon are not the same thing, so we know that the third answer is also incorrect.
By process of elimination, we know that the correct answer must be the last option, but let's still simplify it. 42 miles over 3 gallons simplifies to 14 miles over 1 gallon, or 14 gallons per mile. This is in fact the desired result, so we know that the correct answer is the last option. Hope this helps!
What are the solutions to the quadratic equation below? x^2+34x-72=0
Answer:
( x + 36 ) ( x - 2 ) = 0
Step-by-step explanation:
x^2 + 36x - 2x -72 = 0
x ( x + 36 ) - 2 ( x + 36 ) = 0
( x + 36 ) ( x - 2 ) = 0
SOMEONE HELP PLEASE!! Will make as brainleist!??
Answer:
This is a geometric sequence and the common ratio is equal to ½.
Step-by-step explanation:
For a sequence to be termed to be in arithmetic progression, the difference between consecutive terms are the same and constant.
On the other hand, a sequence is termed to be in geometric progression if the ratio of a term to the term before it is the same as the ratio between the next term to it.
Let's consider the sequence given: 12, 6, 3 . . .
=>Let's try to find the common difference if it would be constant: 6-12 (-6) ≠ 3-6 (-3)
The sequence is not arithmetic.
=>Let's also try to find the ratio of the sequence to see if it is constant:
6/12 (½) = 3/6 (½)
Therefore we can conclude the sequence is geometric because the common ratio (½) is constant.
This is a geometric sequence and the common ratio is equal to ½.
Find an equivalent system of equations for the following system: 3x + 3y = 0 −4x + 4y = −8 PLZ HELP
Answer:
Answer:
3x + 3y = 0
7x - y = 8
Step-by-step explanation:
. Find the measure of angle A.
A
160°
Answer:
20°
Step-by-step explanation:
A= 360°- (160°+2*90°)= 20°
mr rai bys a radio for rs 1880ans sell it to mr Sherpa at 20 percent .how much money does he pay for it
Answer:
Rs 1504
Step-by-step explanation:
Mr. Rai buys for Rs 1880.
He sells it to Mr. Sherpa at 20% discount.
1880 × 20%
= 376
1880 - 376
= 1504
Mr. Sherpa buys it for Rs 1504.
Answer:
Mr. Rai will be receiving $1504 if he sells the radio for 20%.
Step-by-step explanation:
To find a discount, move the decimal over twice on the percentage. After doing this, multiply that number by the original number. You will get a new number. Subtract the price by the new number and there is your answer.
For Example:
20% = .20
1880*.20= 376
1880-376= 1504
There is a simpler way of doing this as well. Multiplying by .8 (which is the remainder of 100% after taking away 20% if this makes sense) will give you the answer immediately. Hopefully this helps.
Good luck!
factorise this expression as fully as possible 2x^2+6x
Answer:
(Factor out 2x from the expression)
2x (x +3)
The radius of a circle is 2 feet. What is the area of a sector bounded by a 180° arc?
Answer:
[tex]\boxed{Area = 3.14 ft^2}[/tex]
Step-by-step explanation:
Radius = r = 2 feet
Angle = θ = π/2 (In radians) = 1.57 radians
Area of Sector = [tex]\frac{1}{2} r^2 \theta[/tex]
Area = [tex]\frac{1}{2} (4)(1.57)[/tex]
Area = 2 * 1.57
Area = 3.14 ft²
Answer:
[tex]\bold{2\pi\ ft^2\approx6,28\ ft^2}[/tex]
Step-by-step explanation:
360°:2 = 180° so the area of a sector bounded by a 180° arc is a half of area of a circle of the same radius.
[tex]A=\frac12\pi R^2=\frac12\pi\cdot2^2=\frac12\pi\cdot4=2\pi\ ft^2\approx2\cdot3,14=6,28\ ft^2[/tex]
Given that 8 <y< 12 and 1<x< 6, find the maximum possible value of
x+y/y-x
Answer:
Step-by-step explanation:
y = {9, 10, 11}
x = {2, 3, 4 , 5}
Maximum value of x + y = 11 + 5 = 16
Minimum value of y -x = 9 - 2 = 7
[tex]\frac{x+y}{y-x}=\frac{16}{7}[/tex]
For the diagram shown, which pairs of angles are vertical angles? Select all that apply. Angle1 and Angle3 Angle2 and Angle4 Angle2 and Angle3 Angle5 and Angle7 Angle5 and Angle8 Angle8 and Angle6
Answer:
2 & 4
1 & 3
5 & 7
8 & 6
Vertical angles are formed in a set of intersecting lines. They are two differrent angles that are opposite of eachother but have the same angle.
Angle pairs that are vertical angles in the diagram shown when a transversal intersects two parallel lines are:
<1 and <3
<2 and <4
<5 and <7; and
<8 and <6
Recall:
Angles that are regarded as pairs of vertical angles share the same vertex and are directly opposite each other at the point of intersection of two straight lines.
From the image given,<1 and <3 are directly opposite each other and share same vertex.
<1 and <3 are therefore are a pair of angles that are vertical angles.
In the same vein, the following pairs:<2 and <4; <5 and <7; and <8 and <6 are all directly opposite each other. They are vertical angles pair.
Therefore, angle pairs that are vertical angles in the diagram shown when a transversal intersects two parallel lines are:
<1 and <3
<2 and <4
<5 and <7; and
<8 and <6
Learn more here:
https://brainly.com/question/2889556
Find the values of the variables and the measures of the angles
Answer:
x = 13
39° and 51°
Step-by-step explanation:
Angles in a triangle add up to 180 degrees.
This is a right angle triangle, so one side has a size of 90 degrees.
3x + 4x - 1 + 90 = 180
7x + 89 = 180
7x = 91
x = 91/7
x = 13
Put x as 13 to work out the size of the angles.
3(13) = 39
4(13) - 1
52 - 1 = 51
Answer:
[tex]x = 13 \\ [/tex]
Measure of the angles
[tex]39 \: \: degrees \\ 51 \: \: degrees[/tex]
Step-by-step explanation:
sum of the interior angles in a triangle= 180°
[tex]3x + 4x - 1 + 90 =1 80 \\ 7x + 89 =1 80 \\ 7x = 180 - 89 \\ 7x =9 1 \\ \frac{7x}{7} = \frac{91}{7} \\ x = 13[/tex]
x = 13,
now lets work out for the angles
[tex]3x \\ 3 \times 13 \\ = 39[/tex]
[tex]4x - 1 \\ 4 \times 13 - 1 \\ 52 - 1 \\ = 51[/tex]
An equilateral triangle has sides 8 units long. An equilateral triangle with sides 4 units long is cut off at the top, leaving an isosceles trapezoid. What is the ratio of the area of the smaller triangle to the area of the trapezoid? Express your answer as a common fraction.
Answer:
1:3
Step-by-step explanation:
Please study the diagram briefly to understand the concept.
First, we determine the height of the isosceles trapezoid using Pythagoras theorem.
[tex]4^2=2^2+h^2\\h^2=16-4\\h^2=12\\h=\sqrt{12}\\ h=2\sqrt{3}$ units[/tex]
The two parallel sides of the trapezoid are 8 Inits and 4 units respectively.
Area of a trapezoid [tex]=\dfrac12 (a+b)h[/tex]
Area of the trapezoid
[tex]=\dfrac12 (8+4)*2\sqrt{3}\\=12\sqrt{3}$ Square Units[/tex]
For an equilateral triangle of side length s.
Area [tex]=\dfrac{\sqrt{3}}{4}s^2[/tex]
Side Length of the smaller triangle, s= 4 Units
Therefore:
Area of the smaller triangle
[tex]=\dfrac{\sqrt{3}}{4}*4^2\\=4\sqrt{3}$ Square units[/tex]
Therefore, the ratio of the area of the smaller triangle to the area of the trapezoid
[tex]=4\sqrt{3}:12\sqrt{3}\\$Divide both sides by 4\sqrt{3}\\=1:3[/tex]
there were 7 little cherries for every 2 big cherries. if there were 630 cherries in the box, how many little cherries were there? (please also answer the question in the picture)
Answer:
1)2205little cherries
2)0.5.
Step-by-step explanation:
1)7little=2big
?=630big
7×630=2205little cherries
2
2)²/5x=¹/10what is the value of 10x-2
first find the value of x that is ¹/10÷²/5=¼
so x is ¼
insert the value ie 10×¼-2
=2.5-2
=0.5
What is the recursive rule for this geometric sequence? 1/2 ,−2, 8, −32,
Answer:
an = an-1 * -4
Step-by-step explanation:
First we need to find the common ratio
r = second term / first term
= -2/ (1/2) = -4
The recursive formula is
an=an−1 * r
an = an-1 * -4
HELP please!!
“Find the volume of the sphere rounded to the nearest hundredth
Answer:
904.32 cm^3
Step-by-step explanation:
The formula for the volume of a sphere is V=4/3πr³. Since r is given, we can plug that in for r. I'm assuming that we are using 3.14 for pi, so when we plug in all the values in the equation we get V = 4/3*3.14*6³, which solves out to 904.32.